What is the relationship between blade inertia and rotor kinetic energy?

As far as I know:

1. High blade inertia provides good pilot intervention time (the time between recognizing engine fail and pushing the collective down).

2. High kinetic energy allows for a soft touch down after flare in autorotation.

What is the relationship between blade's inertia and rotor kinetic energy?

• is this a question about dynamics/kinematics (physics) or there is an actual aviation side of the question? Jun 27, 2014 at 6:52
• @Federico many thanks, I edited my question
Jun 29, 2014 at 15:22
• point c seems a question, not "as far as you know". Jun 29, 2014 at 18:01

The relationship between blade inertia and rotor kinetic energy is:

$$K = N\frac{1}{2}I\omega^2$$ $$I = \int mr^2dr$$

Where:

• $N$ is the number of blades
• $I$ is the moment of inertia of a blade
• $ω$ is the rotational velocity (rotor rpm)
• $m$ is mass
• $r$ is distance from hub along the blade

For a fixed RPM increasing the moment of inertia of the blade increases kinetic energy of the rotor. An increase of the moment of inertia can be obtained by increasing the mass of the blades (inefficient, rotor gets heavy and requries more power from engine, less payload, etc.) or by placing relatively small masses at the tip of the blade.

• should $m$ be $m(r)$? Jun 27, 2014 at 16:14
• @falstro: Absolutely, the mass distribution may change along the blade. I avoided to add the variable to keep the formula less cluttered.
– Emil
Jun 27, 2014 at 16:35
• @Emil, the formula shows us if blade's inertia is high the rotor kinetic energy should be high. Another word blade inertia and rotor kinetic energy are two different terms for the same thing. By the way I referred the Prouty's book. The blade inertia unit is (slug-feet) and rotor kinetic energy unit is (foot-pounds) Am I right?
Jul 9, 2014 at 6:44
• It is possible to have a low Inertia $I$, but combined with a high rotational velocity $\omega$ this will still give a high kinetic energy. Mar 23, 2015 at 13:14

A simple "no math" answer:

The higher the inertia, the more it can "resist" anything that wants to change its velocity.

a. High blade inertia is good pilot intervention time ( the time between engine fail and collective down which army requirement is 2 second.

It usually takes the pilot a few seconds to realize things are going wrong. Call it the "WTF!" moment. A high inertial rotor system will see less decay in speed during those moments. A successful auto-rotation requires preserving that rotor RPM.

b. High kinetic energy is good for soft tough down after flare in autorotation.

So you made it past the "WTF", kept the rotor speed up, picked out your landing spot, and are in full auto-rotation. As you approach the ground you now are going to need to "flare" - increase collective and haul back on the cyclic. The higher inertia rotor system allows for a "sloppier" flare because the inputs (to use the rotors stored energy to arrest the descent) will have less effect on the RPM.

c. What is the relationship between them?

In both cases, the higher inertia system works in the pilots favor.

An extreme example of a high inertia rotor is the (never ending) Carter-Copter Gyro project. They have "weighted" tips to increase rotor inertia. Older video, but jump takeoff demo'd around 40 sec mark. The rotor on an auto-gyro can be "pre-rotated" with some assist from the engine, but when he makes that jump, that is all inertia working in his favor.

• Welcome to Aviation.SE! This is a very nice answer, although some links or sources would make it even better. Perhaps you might consider creating a user account and adding your own questions as well. Jul 2, 2014 at 13:32